To compare the nature of different information obtained using various methods to understand the connectivity of the brain, let us consider a simple model of the brain (Figure A). Assume a brain that has three distinct areas (nodes labeled A–C), with connections originating from each area with the number of connections from one node to another ranging from 1 to 4. For simplicity, let us further assume that a given node is either excitatory (red triangle) or inhibitory (blue square). We will further assume that conflicting signals received from different nodes is resolved by majority vote. For example, if four inhibitory inputs and three excitatory inputs are received, the node will be inhibited. We also assume all nodes are synchronized where τ is the time it takes for each node to trigger the next node and that external stimulation results in an immediate state change at the stimulated node, which allows us to assume a discrete time model where n is the time variable with the discrete time interval τ. While the realistic scenario is obviously much more complex than what is represented here, this simple model brain can help illustrate how different techniques address distinct pieces of the puzzle in our effort to understand the brain circuit. The model brain described above can be summarized with Eq. 1
, where G is the connectivity matrix with entry values that can range from −4 to 4, X(n) and Y(n) are the stimulus input vector and the activity at a given time n with values of 0 (not active) or 1 (active). G will then be a 3 by 3 matrix, X(n) and Y(n) will be 3 by 1 vectors. u is the unit step function applied to each vector components separately.
Figure 3 Tracing brain pathways: simplified model of brain demonstrates nature of the different information obtained using the current state-of-the art methods. (A) Simplified model brain with three distinct areas labeled A–C. Each area has connections (more ...)
For the model brain outlined in Figure A, the G matrix is as follows with a zero-state initial condition.
The tracer methods (Raju and Smith, 2006
) based on viral and/or chemical tracers will provide anatomical information with directionality (Figure B). For example, if an anterograde tracer that does not cross synapses is injected into node A, the injection node will be highlighted with its axonal projections showing nodes that are directly connected with node A (B, C). Different types of tracers, for example, retrograde tracers (Miyamichi et al., 2011
) will give information regarding which nodes the injected region receive axonal projections from. As demonstrated with this example, the tracer-based methods have the advantage of providing information about how different areas are connected with direction and cell type information. However, the main drawback of the method is that it does not allow in vivo
evaluation of the connection, as well as the fact that the number of synapses that can be crossed by existing tracers is limited. Recent developments of powerful tracers with high level of specific control (Wall et al., 2010
) and manganese ion (Mn2+
, Pautler et al., 1998
)-based MRI-sensitive in vivo
fiber tract tracer potentially overcome some of the challenges. While individual tracer methods pose different pros and cons, the main information the tracing methods aims to obtain is the anatomical connectivity with directionality (Gij
) and cell type (+, −).
Diffusion tensor imaging (DTI; Mori and Zhang, 2006
) is an MR technique that relies on the restricted and/or anisotropic zero-displacement diffusion of metabolites (normally the most abundant water molecules are used) within and across different neural compartments (such as intra/extra cellular diffusion and diffusion within the myelin sheath etc.). Signal attenuation is observed whenever diffusion is present along the direction of the magnetic field gradients. The resulting diffusion ellipsoids for each voxel can then be concatenated in order to yield smooth trajectories that are assumed to be co-linear to the primary direction of the physical barriers, which cause the diffusion to be restricted/anisotropic in the first place. With DTI, large-scale connections can be measured without directionality, and without cell type information (Figure C). Due to limitations in spatial resolution and DTI technique’s ability to resolve directional ambiguities when fibers cross, the information that is obtained using DTI will be coarser than those obtained using tracer methods. However, DTI allows in vivo
, non-invasive, and whole brain scanning ability, which enables the assessment of the connections in fully intact brain with the possibility of longitudinal assessment in living humans. Ideally, DTI aims to uncover the larger values of |Gij
| (no direction, cell type information). In Figure C, the DTI image shows connections with |Gij
| values over 3 as an example.
To fully understand the brain, temporal dynamics have to be resolved in addition to the anatomical connections. Traditionally, electrophysiological stimulation and recording hold an important place in the assessment of the activity. For activity assessment in an intact circuit, electrodes are placed in vivo
where cells at a specific location are stimulated and/or recorded. However, one of the most significant difficulties with this approach has been the lack of cell type specificity in the stimulation (Histed et al., 2009
), and the limited spatial information in the readout. With the lack of cell type specificity, it is difficult to interpret the resulting signal while the limited spatial information makes it difficult to trace the activity throughout the brain. fMRI (Ogawa et al., 1992
; Bandettini and Wong, 1997
; Song et al., 2000
), on the other hand, while being a completely non-invasive technique with whole brain spatial information, also lacks cell-type specificity in stimulation with the conventional sensory stimulations and micro-electrode based stimulations (Tolias et al., 2005
). Techniques such as resting-state fMRI (Fox and Raichle, 2007
), while revealing valuable, completely non-invasive information about the network level connectivity, do not provide causal information. Modeling approaches to obtain causal information include the use of granger causality (Goebel et al., 2003
) and dynamic causal modeling (Stephan and Friston, 2011
ofMRI adds valuable new information since causal communication can be directly traced throughout the brain across multiple synapses with global activity pattern information in vivo
. For example, if node A is excited, the downstream impact of such stimulation will be visualized across the whole brain with full spatial information. Assuming a stimulation with 1/6τ Hz, 3τ s duration (where, τ
ms) repeated every 1
min for 20
s duration at node A [Figure D; Table ; X(n)], one can potentially expect positive BOLD signal in all three nodes, since all three nodes will have increased neural activity at 1/6τ Hz with 3τ duration at node A and C and τ duration at node B [Table ; Y(n)]. The amplitude of the ofMRI-measured response at node B could be 3 times smaller than the other nodes since it is three times less active. Alternatively, if continuous stimulation is applied at node A for 20
s every 1
min [Table ; X(n)], one can expect positive BOLD signal in only node A and C since node B will not be active except for a mere τ s at the beginning of the 20-s stimulation [Table ; Y(n)].
As illustrated through this simple example, temporal encoding of the stimulation, in addition to the anatomical connections and cell type, is expected to determine how activity propagates throughout the brain. ofMRI, for the first time, offers the potential to trace such activity throughout the whole brain with temporal accuracy. While the exact relationship between the neural activity and the observed ofMRI signal remains elusive, initial studies show that neural activity patterns are strongly correlated with the ofMRI hemodynamic response function (HRF; Figure 2 in Lee et al., 2010